I too am 6'0" and have been since I was about 14. How old are you?? Because there are TONS of great adult roles that were available in my younger teen years (I'm almost 20 now) when casts we all my age. Mrs. Harcourt in Anything Goes is lots of fun, Dorothy Brock in 42nd Street, Jacquie in Me and My Girl, Dolly in Hello Dolly! Sometimes it matters and sometimes it doesn't. It depends on the director a lot I think.
I've definitely not been cast because of the height difference. I did Bye Bye Birdie and got cast as Mae, even though I read for Rose. The director told me later I would've had it except the kid playing Albert was only 5'6" and it would've looked weird and that it was a ebtter visual if I was the mother.
So, yes, it sucks. But own it and you'll rule the stage!
No Day But Today